show work please In order to find a 87 confidence interval w

show work please

In order to find a 87% confidence interval we need to find values a and b such that for Z ~ N(mu = 0, sigma = 1), P(a

Solution

(a) P(-2.0288<Z<b)=0.87

--> P(Z<b) - P(Z<-2.0288) = 0.87

--> P(Z<b) -0.0212 = 0.87

--> P(Z<b) =0.0212 +0.87 =0.8912

So b= 1.232935

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(b) P(a<Z<2.4926) =0.87

--> P(Z<2.4926 ) -P(Z<a) = 0.87

--> 0.9937 - P(Z<a) = 0.87

--> P(Z<a) =0.9937-0.87 =0.1237

So a= -1.156688